In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation theorem and a functional Schoenberg’s theorem. Following some key results established for the real-valued case, we prove consistency and quantitative central limit theorem for the sample power spectrum operators in the high-frequency regime.
Asymptotics for isotropic Hilbert-valued spherical random fields / Caponera, Alessia. - In: BERNOULLI. - ISSN 1350-7265. - 30:3(2024), pp. 1723-1745. [10.3150/23-BEJ1650]
Asymptotics for isotropic Hilbert-valued spherical random fields
Alessia Caponera
2024
Abstract
In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation theorem and a functional Schoenberg’s theorem. Following some key results established for the real-valued case, we prove consistency and quantitative central limit theorem for the sample power spectrum operators in the high-frequency regime.File | Dimensione | Formato | |
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